The Dwarf Nova PQ Andromedae

In preparation for a parallax study, we obtained a precise J2000.0 astrometric position, corrected for proper motion, from a 2002 October image:

The plate solutions were fit with UCAC–2 stars, and rms residuals were below 0 1. The total error was near 0 1 in each coordinate.

Combining this position with data retrieved and measured from the USNO archives, we obtained a proper motion of

The USNO–B archive alone, without the recent precise CCD image, gives a similar answer: μ_x = +34(6) and μ_y = +24(4) mas yr^-1.

This is a large proper motion, suggesting a fairly nearby star. With our favored velocity ellipsoid for CVs (Thorstensen 2003), the mean distance is 83 pc, with the 16th and 84th percentiles of the distribution at 47 and 148 pc, respectively. However, the distribution is always quite asymmetric (see, e.g., the dashed curve in Fig. 2 of Thorstensen 2003), so the most probable distance is ∼120 pc.

In 2005 January we obtained four consecutive nights of time‐series photometry, using a CCD imager on the MDM 1.3 m telescope. We used a broadband (3800–8000 Å) filter and several integration times in the range 40–60 s. PQ And showed no obvious variability in its light curve, staying always close to V = 18.5 ± 0.4. (The error was large because the passband was so broad.)

To search for periodic signals, we calculated the power spectrum of the four‐night light curve. The result is seen in the upper frame of Figure 1. Two obvious periodic signals are flagged, at 68.41(5) and 136.36(5) c/d.⁷ The complex of power near 36 c/d is likely to contain a third signal—probably at 35.70(6) c/d, although the alias at 36.70 c/d is a viable and worthy alternative. The lower frames contain close‐ups of these three signals, and synchronous summations. In the case of the signal at lowest frequency, we summed at half the detected frequency (i.e., 17.85 c/d)—because there was a weak complex near the 18/19 c/d subharmonic, and because double‐humped orbital waveforms are very common in low‐ M ˙ dwarf novae. Naturally, the summation at 0.0560 days (17.85 c/d) does show a double‐humped waveform. We refer to it as the "orbital" waveform, although the hypothesis of an orbital origin is unproven.

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Vanlandingham et al. (2005) also report evidence for these three signals, although at a frequency resolution too low to clarify the issue of the commensurability of the frequencies. So they are presumably long‐lived features in the star.

We observed PQ And several times with calibrated photometry. On the nights of 2004 January 17 and 28, we observed with the 1.0 m reflector of the US Naval Observatory. We found the star respectively at V = 19.24(8), B = 19.25(8) and at V = 18.94(10), B = 19.07(13). This yields a mean of V = 19.10, B - V = 0.07. Our estimate during 2005 January was slightly brighter, so we adopt V = 18.95. The total Galactic reddening on this line of sight is E(B - V) = 0.06 (Schlegel et al. 1998); and for distances near 200 pc, most of this reddening is probably also on the line of sight to PQ And. Assuming A_v = 3E(B - V), we adopt A_v = 0.15 mag and hence a dereddened V = 18.8.

Infrared photometry was obtained on 2005 January 20 with the Simultaneous Quad Infrared Imaging Device (SQIID) on the 2.1 m telescope at Kitt Peak National Observatory. The camera records J, H, K, and L images simultaneously, although we found that the L data were of insufficient quality to be useful. JHK data were all of good quality and were obtained synchronously with 5 × 8 s exposures obtained at each of 10 dithered positions. The images were combined to produce a sky image that was subtracted from each target image before combining them into an average for each band. Each of these averages preserved an image quality better than 1 4. Sensitivity variations were corrected with twilight sky flats in the usual manner.

PQ And was adequately detected in all filters. Standard aperture photometry was used to extract differential magnitudes of the target relative to several 2MASS (Two Micron All Sky Survey) stars in the field, all of which were near 14th magnitude in J, H, and K—well exposed and with 2MASS errors of less than 0.05 mag. The derived magnitudes of PQ And were J = 18.57(13), H = 17.97(11), and K = 17.45(10), where the uncertainties are dominated by statistics of the PQ And measurement itself.

WZ Sge stars typically become very faint in quiescence, with the visual light dominated by the white dwarf. The broad Balmer absorptions in PQ And certainly support this. In addition, the noncommensurability of the 68 and 136 c/d photometric signals strongly suggest an origin in nonradial pulsations of the white dwarf—indicating again that the white dwarf dominates the light. We estimate that ∼75% of the quiescent V light comes from the white dwarf, with the remainder coming mostly from accretion (because of the likely double‐humped orbital signal, and because of the nightly variability). This implies V = 19.1 for the white dwarf, and V = 20.3 for accretion light.

The white dwarf's temperature was measured by Schwarz et al. (2004) as 12,000 ± 1000 K, and a similar temperature is suggested by the presence of white‐dwarf pulsations, assuming the white dwarf to be like ordinary ZZ Cet stars (T_eff = 11,500 ± 600 K; Mukadam et al. 2004). White dwarfs in CVs average ∼0.8 M_⊙, which implies M_v = 12.4 for this T_eff. Thus, we estimate a "white dwarf parallax" of 220(60) pc.

The dwarf‐nova outburst itself also provides a distance estimator. Supermaxima of 80 minute SU UMa–type dwarf novae (the parent class of the WZ Sge subclass) should reach M_v∼4–5 (Warner 1987; Cannizzo 1998; Harrison et al. 2004), which suggests a distance of 140(50) pc.

A third constraint comes from proper motions, which we discuss above and roughly characterize as 110(50) pc. An average of these three constraints implies a final distance estimate of 150(50) pc.

Because PQ And appears so similar to WZ Sge, a star of precisely known distance (43 ± 3 pc; Thorstensen 2003; Harrison et al. 2004), we can also try to use WZ Sge to scale the distances. The respective dereddened white‐dwarf components have V = 19.1 and 16.2, and the dwarf novae at maximum have V = 10.0 and 8.0. These suggest that the distance moduli differ by 2.4(5) mag, implying d = 130(30) pc. A second useful comparison star is GW Lib, another WZ Sge–type dwarf nova—with a similar quiescent spectrum and light curve (including nonradial pulsations, certifying a similar T_eff for the white dwarf; van Zyl et al. 2004). Trigonometric parallax yields a distance of 105(20) pc to GW Lib (Thorstensen 2003). The white‐dwarf components have V = 19.1 and 17.7 in PQ And and GW Lib, and the dwarf novae at maximum have V = 10.0 and 8.5, respectively. Comparison suggests d = 200(60) pc for PQ And.

These are consistent with our estimated 150(50) pc. That's our story, and we're sticking to it.

The dereddened flux distribution is shown in Figure 2. The points show the BVJHK measurements, and the curve shows the flux distribution of the pulsating white dwarf G226–29. The two flux scales differ by a factor 560, which sets the G226–29 V point at that of the estimated white‐dwarf component in PQ And (75% of the total). Thus, the curve represents our estimate of the full flux distribution of the white dwarf in PQ And, and the difference between points and curve represents other components (secondary star and accretion light).⁸ As shown in Figure 2, that difference is roughly constant at ∼0.035 mJy from K through B bands, with possibly a little turn‐up at H and K.

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Accretion light in such stars is likely to be optically thin emission, with T∼5000–7000 K (Williams 1980; Tylenda 1981), and at low frequency this typically shows a spectral slope F_v∝v⁰. This seems to be the main lesson of Figure 2 also: the second component in PQ And is very likely the accretion disk, with its attendant "hot spot."

Still, the possible HK turn‐up leaves room for some contribution by a cool secondary. After subtracting the K contribution of the white dwarf and a minimal estimate for accretion light (extrapolating from BV measurements), we estimate from Figure 2 that perhaps half of the K light could come from the secondary. This leaves an upper limit of K = 18.2(3) for the secondary, or M_K>12.3(6) at the estimated distance.

This is probably too faint to be a main‐sequence star. At the end of the (core hydrogen burning) main sequence at 0.075 M_⊙, model stars have M_K = 11.4 at an age of 10 Gyr, and M_K = 10.8 at 1 Gyr (Baraffe et al. 1998). It is not obvious which age is appropriate to use for a CV secondary, which is "ageless," since it does not evolve on a single‐star timescale. However, secondaries burning hydrogen in their cores must be at least as bright as a "ZAMS" model (10 Gyr for low‐mass stars), because the quirks of CV evolution (mainly the lingering effects of energy deposition in the envelope from prior evolution and heating episodes) can only add to this luminosity. Thus, we conclude that the secondary is essentially "substellar"; i.e., with M₂<0.075 M_⊙.

The accretion light is also very faint, at M_v = 14.4(9). This is among the faintest accretion components seen among CVs, and further emphasizes the likelihood that PQ And is a period bouncer—an old CV that has evolved past minimum period and cannibalized its secondary down to M₂<0.075 M_⊙ (PTK, especially their Table 4).

Our estimates of distance and (therefore) luminosity are in conflict with those given by Schwarz et al. (2004), who fit the absorption‐line profiles to a model white dwarf and found T_eff = 12,000 K, log g = 7.7, and d = 330(50) pc. We are inclined to distrust such fits for white dwarfs in CVs; T_eff is straightforward if the white dwarf dominates the flux, but log g depends on high‐quality spectra in the line wings, plus the assumption that line wings are uncontaminated by emission components (or a way to identify and subtract those components). In particular, the three Balmer lines used by Schwarz et al. are all threatened by He i emission lines in their wings, plus the broad base of Balmer emission (unmeasurable, but still in principle contaminating the profiles). And judging from the strength of the He i λ5876 emission in Figure 1 of Schwarz et al., we reckon that the weaker He i lines are significant contaminants. Fill‐in of the absorption would lower the apparent log g. An undesired and unsubtracted continuum flux (from accretion, which we reckon at ∼25% from the putative orbital signal) would also bias the result toward lower gravity. So we suspect that Schwarz et al. deduced too low a gravity, and prefer to merely assign an M_v appropriate for a nominal 0.8 M_⊙ (Webbink 1990; Smith & Dhillon 1998) white dwarf, along with the 12,000 K reasonably certified by the pulsations. The latter also yields a distance much more compatible with other methods of estimation (proper motion and the dwarf‐nova outburst).

Schwarz et al. quote another distance estimate even more discrepant from ours: a lower limit of 319–817 pc from the observed K flux. This is from an application of the "Bailey method": assuming that the secondary is of known surface brightness, in this case appropriate for a M5–M7 secondary (S_K = 5.5 ± 0.5; Ramseyer 1994). We have no quarrel with Bailey's method, but the very short orbital period that we favor (80 or 78 minutes, compared to ∼100 minutes in Schwarz et al.) greatly changes the resulting distance estimate.

Bailey's method uses the secondary's radius R₂, surface brightness S_K, and K magnitude to yield the distance d in pc:

PQ And is essentially at the minimum P_orb for hydrogen‐rich secondaries, implying a secondary at or beyond the end of the main sequence. The value of S_K for such stars is unknown, and probably differs very greatly if the star has ceased nuclear burning. In short, the Bailey method is uncalibrated in this regime. In WZ Sge, for example, where all parameters on the right side of the equation are specified by observation (K>16, d = 43, R₂ = 0.09), we obtain S_K>7.8. If we adopt K = 18.2 and apply this to PQ And (not unreasonable, since the two stars are apparently so similar in P_orb), we would obtain d<125 pc.

J. P. acknowledges financial support from NSF grants AST‐0098254 and AST‐0406813, and J. R. T. acknowledges support from NSF grants AST‐9987334 and AST‐0307413. R. H. gratefully acknowledges the assistance of Kevin Pearson and Dawn Gelino in obtaining the infrared photometry. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by NASA and the NSF. It has also made use of the USNOFS Image and Catalogue Archive operated by the US Naval Observatory, Flagstaff Station.